(1) Your <script>
tag should be placed before the closing </body>
tag. Your JavaScript is trying to manipulate HTML elements that haven't been loaded into the DOM yet.
(2) Your assignment of HTML content looks jumbled.
(3) Be consistent with the case in your element ID, i.e. 'DIV2' vs 'Div2'
(4) User lower case for 'document' object (credit: ThatOtherPerson)
<body>
<div id="DIV1">
// Some content goes here.
</div>
<div id="DIV2">
</div>
<script type="text/javascript">
var MyDiv1 = document.getElementById('DIV1');
var MyDiv2 = document.getElementById('DIV2');
MyDiv2.innerHTML = MyDiv1.innerHTML;
</script>
</body>
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